Localized to Itinerant Electronic Transitions in Transition-Metal Oxides

Uσ condition transforms the crystal-field e orbital into itinerant-electron orbitals of a narrow σ* band. Mössbauer data15a have revealed a progres...
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Chem. Mater. 1998, 10, 2980-2993

Localized to Itinerant Electronic Transitions in Transition-Metal Oxides with the Perovskite Structure J. B. Goodenough* and J.-S. Zhou Center for Materials Science & Engineering University of Texas at Austin, Austin, Texas 78712-1063 Received April 13, 1998. Revised Manuscript Received June 16, 1998

The transition from localized to itinerant electronic behavior is shown to be first-order. In a perovskite, segregation into localized-electron and itinerant-electron phases can be accomplished by cooperative atomic displacements. Sr1-xCaxVO3 and La1-xNdxCuO3 illustrate single-valent perovskites that exhibit localized-electron fluctuations in an itinerant-electron matrix on approaching the Mott-Hubbard transition, and CaFeO3 and NdNiO3 form chargedensity waves with MO complexes or itinerant-electron slabs alternating with localizedelectron states.

Contents

I. II. III. IV. V.

Introduction Structural Considerations Electronic Considerations Oxygen Displacements Representative Single-Valent Perovskites

1 1 3 5 6

I. Introduction This review addresses crossovers from localized to itinerant electronic behavior in AMO3 stoichiometric oxides with the perovskite structure that contain a single first-long-period transition-metal atom M. The larger A atoms in these structures are lanthanide or yttrium and/or alkaline-earth atoms. The perovskite structure allows extensive cation substitutions as well as the introduction of vacancies at any atomic site; it is also able to adapt to a mismatch of the equilibrium A-O and M-O bond lengths. This flexibility allows extensive chemical substitution and/ or deviation from oxygen stoichiometry. This review is restricted to stoichiometric and single-valent MO3 arrays in which M is a transition-metal atom. Appropriate substitutions of isovalent A cations of different size are used to change hexagonal polytypes or to modulate the bending angle φ of the dominant (180° - φ) M-O-M interatomic interactions within a pseudocubic MO3 array. Modulation of the angle φ and/or the oxidation state of the MO3 array can, in several cases, induce a transition from localized to itinerant 3d electrons at first-long-period transition-metal atoms M. Substitution of an aliovalent A cation also changes the oxidation state of the MO3 array from single-valent to mixedvalent, but in this review we focus attention on singlevalent MO3 arrays. An adequate description of a localized-to-itinerant electronic crossover is confronted with the need to consider not only strong electron correlations and spinspin interactions, but also strong electron interactions with oxygen atom vibrations. Where the latter interac-

tions result in a static charge-density wave (CDW) or a cooperative Jahn-Teller (J-T) deformation, the characteristics of the interactions can be clarified by a diffraction experiment. However, experiments designed to sort out the characteristics of the electron-lattice interactions in a dynamic situation are confronted by time scales τ < 10-12 s, which are too short for a conventional diffraction experiment. Nevertheless, there is mounting indirect evidence that dynamic electronlattice interactions are dominant if J-T or pseudo-J-T deformations can occur at some of the M atoms of the MO3 arrays, and fast experimental probes are beginning to provide more direct information on how these interactions organize the electronic and vibrational components into vibronic states within a three-dimensional MO3 array or a two-dimensional MO2 sheet in an intergrowth structure. We introduce structural and electronic considerations needed to interpret the properties of the transitionmetal oxides with perovskite-related structures, including the cooperative oxygen displacements that are encountered, before we present relevant data for several systems that approach or undergo a transition from localized to itinerant electronic behavior. II. Structural Considerations A. Tolerance Factor. Figure 1a shows the ideal AMO3 cubic-perovskite structure. Matching of the equilibrium A-O and M-O bond lengths would correspond to a geometrical tolerance factor

t ≡ (A-O)/x2(M-O) ) 1

(1)

where the equilibrium bond lengths are normally calculated for room temperature and atmospheric pressure from the sums of ionic radii; the radii have been obtained from X-ray diffraction data and are available in tables.1 In the oxygen-stoichiometric perovskites to be discussed, the MO3 array contains a single M atom and no vacancies, but the t factor and the oxidation state of the MO3 array are varied by introducing A cations of

10.1021/cm980276u CCC: $15.00 © 1998 American Chemical Society Published on Web 10/02/1998

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Figure 1. (a) The ideal cubic and (b) the orthorhombic AMO3 perovskite structure.

Figure 2. Perovskite polytypes: (a) cubic, (b) hexagonal 2H, (c) hexagonal 6H, (d) hexagonal 4H, and (e) rhombohedral 9R. Octahedral sites share corners in cubic stacking, faces in hexagonal stacking of close-packed AO3 planes.

different size and charge. With mixed A cations and a mixed valence on the MO3 array, averaged equilibrium bond lengths are used in eq 1. At t < 1, the M-O bonds are under compression and the A-O bonds are under tension. The lattice relieves these stresses by cooperative rotations of the cornershared MO6 octahedra about a cubic crystallographic axis, which bend the M-O-M bond angles from 180° to (180° - φ) and reduce the number and length of the shortest A-O bonds.2 These cooperative rotations also reduce the crystal symmetry: rotations about a [001] axis give tetragonal symmetry I4/mcm, those about a [111] axis give rhombohedral (R3 h c) symmetry, those about a [110] axis give orthorhombic (Pbnm or Pnma) symmetry (Figure 1b), and those about a [101] axis give orthorhombic (Imma) symmetry.3 The most common structures are rhombohedral and orthorhombic. Phase transitions involving oxygen-atom displacements away from one M atom near neighbor toward the other are superimposed on these cooperative rotations.

At t > 1, the A-O bonds are under compression and the M-O bonds are under tension; these stresses are relieved by a change from cubic to hexagonal stacking of the AO3 close-packed planes of Figure 1a.4 Hexagonal stacking introduces columns of face-shared MO6 octahedra that are bound to one another only by A-O bonds, which eliminates any problem with bond-length mismatch. However, stronger electrostatic Mm+ - Mm+ repulsive interactions occur across shared octahedralsite faces, so the perovskite structure changes with increasing t > 1 from all-cubic to all-hexagonal stacking of AO3 planes by the series of hexagonal polytypes illustrated in Figure 2. In the 6H and 4H structures, pairs of face-shared octahedra allow c-axis displacements of the Mm+ cations from the centers of their octahedra to reduce the electrostatic repulsions between them; in the 9R polytype, units of three face-shared octahedra allow the outer two Mm+ cations to be displaced along the c-axis. More complex polytypes may

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segregation into an itinerant-electron phase and a localized-electron phase can be expected at a first-order crossover. In the MO3 array of a perovskite, such a phase segregation can be stabilized at temperatures too low for atomic diffusion by cooperative oxygen-atom displacements that create shorter and longer M-O bond lengths. These cooperative oxygen displacements may be long-range and static or short-range and dynamic (see section IV). III. Electronic Considerations

Figure 3. Ba1-xSrxRuO3 P - x phase diagram; P ) hydrostatic pressure.

be found where aliovalent A cations of different size are present. The thermal expansion and the compressibility of the A-O bond are normally larger than those of the M-O bond, which is made evident by the relations

dt/dT > 0

and

dt/dP < 0

(2)

The normal pressure dependence dt/dP < 0 has been demonstrated by transforming under pressure hexagonal polytypes to phases with more cubic stacking,5 as is illustrated in Figure 3. However, at a crossover from localized to itinerant electronic behavior or from a highspin to a low-spin configuration, a dt/dP > 0 is found and is a critical aspect of these crossovers. B. Virial Theorem. For central-force fields, the virial theorem of mechanics becomes

2〈T〉 + 〈V〉 ) 0

(3)

and a change from localized to itinerant electronic behavior corresponds to a decrease in the mean kinetic energy 〈T〉 of the electronic system that must be compensated by a decrease in the magnitude of the mean potential energy |〈V〉| of the electrons. The d-like electrons of an MO3 array that undergo such a change occupy antibonding states, so a shortening of the M-O bond decreases |〈V〉| and is associated with a change from localized to itinerant electronic behavior.6 A global change from localized to itinerant electronic behavior would give a discontinuous change in 〈T〉, and the corresponding discontinuous change in 〈V〉 would result in a discontinuous change in the equilibrium M-O bond length and hence in a first-order phase change. In this case, the M-O bond energy has a double well at crossover, and the localized-electron phase has an anomalously large compressibility of the M-O bond, which makes dt/dP > 0. Moreover, a

A. Valence Electrons and 4fn Configurations. The ionic Madelung energy of an AMO3 perovskite stabilizes filled bonding bands that are primarily O-2p in character and are separated from antibonding, primarily cationic s and p bands by a large (∼6 eV) energy gap. Lanthanide A cations Ln introduce empty 5d states that overlap the antibonding s bands.7 The 4fn configurations at the Ln atoms are localized, and the intraatomic electron-electron coulomb energies U separating 4fn and 4fn+1 configurations are large, U > 5 eV. Consequently the Ln atoms can have only a single valence state unless a 4fn configuration falls in the energy gap between the filled O-2p bands and the empty antibonding bands.8 However, Ce4+ is too small to occupy the A site of a perovskite and the Eu2+:4f7 level, which is stable relative to the bottom of the 3d band in EuTiO3, lies above the Fermi energy in the other EuMO3 oxides containing first-long-period transitionmetal atoms M.9 In the perovskite-related oxides to be discussed, only the Pr:4f2 level lies close enough to the Fermi energy F of a partially filled band to pose any ambiguity about the valence state of the Ln cation, and this ion only in the presence of the Cu(III)/Cu(II) couple.10 The examples discussed next all contain Ln3+ ions with localized 4fn and 4fn+1 configurations well removed from the Fermi energy. B. M-3d Electrons. In the AMO3 perovskites containing a first-long-period transition-metal atom M, the M-3d electrons may be either localized or itinerant.11 To understand this phenomenon, we begin with the construction of crystal-field 3d orbitals and then consider the nature of the interactions between localized crystal-field configurations on neighboring M cations and how the crystal-field approximation breaks down. 1. Crystal-Field Considerations. The five 3d orbitals of a free atom are degenerate; but with more than one electron or hole in the 3d manifold, the spin degeneracy is removed by the ferromagnetic direct-exchange interactions between electron spins in orthogonal atomic orbitals. The energy splitting between localized spin states will be designated ∆ex. The atomic orbitals fm with azimuthal orbital angular momentum operator Lz, where Lzfm ) -ip(∂fm/∂φ) ) (mpfm, have the angular dependencies

f0 ∼ (3 cos2 θ - 1) ∼ [(z2 - x2) + (z2 - y2)]/r2 f(1 ∼ sin 2θ exp((iφ) ∼ (yz ( izx)/r2 f(2 ∼ sin2 θ exp((i2φ) ∼ [(x2 - y2) ( ixy]/r2

(4)

In an octahedral site, the xy and (yz ( izx) orbitals only overlap the neighboring O-2pπ orbitals, whereas the [(z2

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Figure 4. Octahedral-site energies of empty d states of unoccupied Mn3+/Mn2+ redox couple relative to the valenceband edge. Note: Mn3+:t3e1 configuration has 2-fold e-orbital degeneracy; Mn2+:t3e2 would be high-spin (∆ex > ∆c) and Mn4+: t3e0 would have t3(v) and e0(v) manifolds lowered by Uπ and Uσ, respectively, with Uπ > Uσ.

- x2) + (z2 - y2)] and (x2 - y2) orbitals only overlap the O-2s, 2pσ orbitals. The resonance integrals bca ≡ (fm, H′φO) ≈ mO(fm, φO) describing the energy of charge transfer to the empty M-3d orbitals from the samesymmetry sum of near-neighbor oxygen orbitals φO contain both an overlap integral (fm, φO) and a oneelectron energy (mO) that are larger for σ-bonding than for π-bonding. Therefore, the antibonding states of a σ-bond are raised higher in energy than those of a π-bond and, as a consequence, the cubic symmetry of the octahedral site raises the 2-fold-degenerate pair of σ-bonding e orbitals, the [(z2 - x2) + (z2 - y2)] and (x2 y2) orbitals, above the 3-fold-degenerate set of π-bonding t orbitals xy, (yz ( izx) by an energy ∆c and quenches the orbital angular momentum associated with m ) (2 (see Figure 4). If the empty 3d orbitals of a degenerate manifold lie an energy ∆Ep above the O-2p orbitals and ∆Es above the O-2s orbitals, the antibonding d-like states may be described in second-order perturbation theory to give the crystal-field wave functions

ψt ) Nπ(ft - λπφπ)

m ) 0, 0

(5)

provided the covalent-mixing parameters are λπ ≡ bπca/ ∆Ep , 1 and λσ ≡ bσca/∆Ep , 1. A larger ∆Es keeps λs , 1, where eq 5 is applicable. If ∆Ep becomes too small or becomes negative, the perturbation expansion breaks down and an isolated MO6 complex must be described by molecular-orbital (MO) theory. According to the second-order perturbation theory, the antibonding states are raised by the M-O interactions an energy

∆ ) |bca|2/∆Ei

Uπeff ) Uπ

for n ) 1 or 2; n ) 4 or 5 with ∆c > ∆ex; n ) 6 or 7 with ∆ex > ∆c

) Uπ + ∆ex

Uσeff ) Uσ

for n ) 3 with ∆c > ∆ex; n ) 5 with ∆ex > ∆c

for n ) 4 with ∆ex > ∆c; for n ) 7 or 9 with ∆c > ∆ex

) Uσ + ∆c ) Uσ + ∆ex

for n ) 3 with ∆ex > ∆c; for n ) 6 with ∆c > ∆ex for n ) 8

(8)

2. Interatomic Interactions. In the perovskite structure, the separation between next-near-neighbor M atoms is too large for significant M-M ψt-orbital interactions; the dominant interactions between d-like orbitals centered at M atoms are the (180° - φ) M-O-M interactions. The spin-independent resonance integrals for these interactions are

bπcac ≡ (ψti, H′ψtj) ≈ πλπ2

m ) 0, (1

ψe ) Nσ(fe - λσφσ - λsφs)

orbitals with the empty A-cation wave functions, which lowers the magnitude of an effective λπ and increases ∆c. The cubic-field splitting ∆c is the same order of magnitude as the intraatomic exchange energy ∆ex, and the d4 - d7 configurations may be either high-spin t3e1, t3e2, t4e2, and t5e2, where ∆ex > ∆c, or low-spin t4e0, t5e0, t6e0, and t6e1, where ∆c > ∆ex. The covalent mixing of O-2p wave functions into ψt and ψe lowers the intraatomic electron-electron coulomb energies, which makes Uσ < Uπ; it also lowers the intraatomic exchange splitting ∆ex and increases ∆c. Therefore, stronger covalent mixing stabilizes low-spin relative to high-spin configurations. Moreover, the effective energy Ueff required to add an electron to a dn manifold to make it dn+1 must take into account ∆c as well as ∆ex:

(6)

and the cubic-field splitting is

∆c ) ∆σ - ∆π ) ∆M + (λσ2 - λπ2)∆Ep + λσ2∆Es (7) where ∆M is a purely electrostatic energy that is small and of uncertain sign due to the penetration of the O2ion electron cloud by the crystal-field wave functions. Omitted from eqs 5 and 7 is the interaction of the ψt

bσcac ≡ (ψei, H′ψej) ≈ σλσ2 cos φ

(9)

where λπ varies with the acidity of the A cation as well as with φ. In the absence of a localized spin on the M atoms, the tight-binding bandwidths for these interactions are

Wπ ≈ 2zbπcac

and

Wσ ≈ 2zbσcac

(10)

where the number of like nearest neighbors is z ) 6 for an MO3 array. Because λσ > λπ and φ is small, it follows that

Wσ > Wπ

(11)

A Wπ < Ueff relationship can leave a tn manifold localized whereas a Wσ > Uσeff relationship transforms localized e orbitals into an antibonding σ* band of itinerantelectron states. It is thus apparent that a high-spin 3d4 configuration, which has Uπeff ) Uπ + ∆c > Uσeff ) Uσ, may satisfy the condition Wπ < Uπeff and Wσ > Uσeff, in

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which case a localized t3 configuration coexists with a partially occupied, narrow σ* band of e-orbital parentage.12 Where ∆Ep ≈ 0, the perturbation expansion leading to eq 5 is not applicable. In this case, the covalent mixing of M-3d and O-2p states is so extensive that band theory must be used. Nevertheless, covalent mixing gives the antibonding orbitals d-like symmetry and raises them to the top of the O-2p bands. What changes at the crossover ∆Ep ≈ 0 is the spectral weight in the antibonding bands from primarily M-3d to primarily O-2p character. Where this happens in a single-valent semiconductive oxide, the energy gap from the top of the filled bands to the lowest unoccupied redox energy has been referred to as a charge-transfer gap ∆ as opposed to an intraatomic Ueff.13 However, where the spectroscopist identifies a ∆ as against a Ueff, further oxidation of a perovskite MO3 array does not normally introduce holes into bonding or nonbonding O-2p bands, but into a strongly hybridized antibonding band of d-like symmetry. However, a ∆Ep ≈ 0 can manifest itself in the formation of molecular orbitals in metal-oxygen clusters or by the formation of itinerant M-3d electrons in antibonding π* or σ* bands IV. Oxygen Displacements A. Single-Valent MO3 Arrays. In a single-valent MO3 array, a variety of long-range cooperative oxygen displacements away from one M-atom near neighbor toward the other have been found. These displacements are superimposed on the cooperative MO6 rotations associated with a t < 1. They require a negative curvature of the d-electron potential-energy curve φ(R) at the equilibrium bond length Req for the total potentialenergy curve Φ(R). In this case, ∆d ≈ (1/2)(∂2φ/∂R2)δ2 ) -Aδ2 (where δ is the oxygen displacement) gives an energy gain for the d-like electrons at a cost in elastic energy ∆d ) Bδ2 > 0, and the total energy gained is14

∆ ) -(A - B)δ2

(12)

An oxygen-atom displacement can only be stabilized where A ) -(1/2)(∂2φ/∂R2)Req > B. This condition requires, in addition to an A > 0, a relatively small B, and hence a large compressibility of the M-O bond at Req, as occurs where the M-O bond has a double-well potential energy.6 Shortening an M-O bond increases the M:3d-O:2p covalent mixing and raises the energies of the antibonding d-like states; lengthening an M-O bond lowers the energies of these states. Where the 3d orbitals of the M cations are empty, as in BaTiO3, no energy is gained by raising some d orbitals and lowering others, so the cooperative oxygen displacements create alternating long and short bonds ‚‚‚M-O‚‚‚M-O‚‚‚ on opposite sides of every M cation, thereby stabilizing the occupied O-2p bonding states at the expense of the empty, antibonding d states. The resulting displacement of each M cation from the center of symmetry of its site results in a ferroelectric or antiferroelectric phase. Such displacements are possible with d0 or d1 configurations. However, where the cation has more than one d electron, the cooperative oxygen displacements leave the M cations in the center of symmetry of their site; these

displacements either order the electrons among initially degenerate, localized orbitals within an atom or transfer electrons from M atoms in a molecular-orbital cluster to a localized-electron configuration on a neighboring M atom. Three such situations can be distinguished: disproportionation, ordering of high-spin and low-spin configurations, and J-T distortions. Disproportionation. Cooperative oxygen displacements that shorten all the M-O bonds at every other transition-metal atom MI and lengthen all the M-O bonds on the neighboring MII atoms can occur in an MO3 array. Stronger covalent bonding within MIO6 complexes and more ionic bonding to MII cations raises the antibonding d-like states of a complex relative to those at the MII cations by an energy ∆E. A ∆E > Ueff condition would result in an electron transfer from the MIO6 complex to the MII cations. Such a disproportionation reaction creates a CDW in the crystal, and the physics literature refers to this phenomenon as a “negative-U” CDW because of a (Ueff - ∆E) < 0 relationship. Such a CDW changes the periodicity of the electronic potential so as to open an energy gap at the Fermi energy. Disproportionation is found in the perovskite CaFeO3, which contains high-spin Fe4+:3d4 ions. A Wπ < Uπ + ∆c condition leaves the t3 configuration localized, whereas a Wσ > Uσ condition transforms the crystal-field e orbital into itinerant-electron orbitals of a narrow σ* band. Mo¨ssbauer data15a have revealed a progressive splitting of the Fe4+ ion spectrum with decreasing temperature below 290 K toward equal populations of Fe(V)O6 complexes and octahedral-site Fe3+ ions. The associated oxygen displacements have been confirmed.15b In CaFeO3, the σ* band is narrow enough to satisfy eq 12, whereas in isoelectronic SrFeO3, which has a larger M-O-M bond angle (180° - φ), the high-spin, metallic configuration t3σ*1 does not disproportionate to lowest temperatures. Jahn-Teller Distortions. The single-valent perovskite LaMnO3 contains an MO3 array that is isoelectronic with CaFeO3 and SrFeO3, but a Wσ < Uσ relationship retains a localized t3e1 configuration at the high-spin Mn3+ ions. In this case, more energy is gained by a cooperative deformation of the octahedral sites from cubic to orthorhombic symmetry that lifts the e-orbital degeneracy; the intraatomic ordering of electrons among localized orbitals does not require an e-orbital splitting ∆E > Uσ; it occurs among localized orbitals where Uσ is large. Neutron diffraction data16 have confirmed the predicted17 intraatomic orbital ordering by cooperative oxygen displacements within orthorhombic (001) planes that create long O‚‚‚Mn‚‚‚O bonds alternating with short O-Mn-O bonds within an a-b plane. Ordering of High-Spin and Low-Spin Configurations. An intraatomic transition from a low-spin to a highspin state represents an intraatomic reordering of electrons among d-like orbitals that requires a change in Req without requiring a change in site symmetry. A greater entropy ∆S is associated with a high-spin state, and the thermal energy T∆S can drive a low-spin-tohigh-spin transition with increasing temperature. The transfer of antibonding electrons from π-bond to σ-bond orbitals increases Req at the high-spin cations MHS. In an MO3 array, the elastic energy associated with a

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larger Req at MHS cations can be minimized by retaining low-spin MLS cations as near neighbors, which involves oxygen displacements MHS‚‚‚O-MLS. A short-range ordering of MHS and MLS cations on alternate M sites of an MO3 array may be anticipated where the MHS: MLS ratio approaches 50:50. Such ordering would inhibit M-O-M interactions from forming itinerant σ*band states until the population of the high-spin ions exceeds 50:50. A greater high-spin population would introduce a compressive stress within high-spin clusters that can be relieved, according to the virial theorem, by a delocalization of the σ-bonding electrons first within isolated clusters and only at higher high-spin concentrations over the entire crystal. This situation is illustrated by the perovskite LaCoO3, which contains only low-spin Co(III):t6σ*0 configurations at lowest temperatures.18a However, localized intermediate-spin configurations t5e1 are excited rather than high-spin Co3+:t4e2.18b The population of localizedelectron configurations increases progressively with increasing temperature, with a larger Req at a trivalent cobalt stabilizing localized e1 configurations. A 50:50 intermediate-spin:low-spin population is approached by room temperature, and above room temperature there is a smooth transition from a semiconductive to a metallic state. The low-spin-to-intermediate-spin transition can be followed by magnetic susceptibility, but the fluctuations between high-spin and low-spin neighbors become fast relative to 10-8 s already below room temperature, which has prevented Mo¨ssbauer spectra from demonstrating a plateau in the increase in localized intermediate-spin population with temperature at the 50:50 distribution.19 Such fluctuations cannot be detected by a diffraction experiment. An anomalously large thermal expansion coefficient extending to highest temperatures indicates that the population of σ*-band electrons continues to increase with temperature until after the metallic state is realized.20 B. Mixed-Valent MO3 Arrays. In a mixed-valent MO3 array, cooperative oxygen displacements “dress” localized-electron charge carriers. These carriers move diffusively, carrying the local deformations with them. These dielectric polarons are to be distinguished from magnetic polarons. Magnetic polarons are itinerantelectron charge carriers that become confined to regions of short-range ferromagnetic order above a ferromagnetic Curie temperature; they carry a multi-atom volume of ferromagnetic order through a paramagnetic matrix. A nonadiabatic dielectric polaron is normally confined to a single cation site by the shortening or lengthening of all the M-O bonds at that site; shortening confines a mobile hole and lengthening a mobile electron. At a first-order crossover from localized to itinerant electronic behavior, cooperative oxygen-atom displacements may segregate hole-rich from electron-rich domains. In this case, hole-rich clusters contain molecular d-like orbitals within an electron-rich matrix of localized electrons or electron-rich clusters of localized electrons are segregated from a hole-rich matrix containing itinerant electrons. If these clusters are mobile, they represent nonadiabatic polarons containing more than one cation site.

Chem. Mater., Vol. 10, No. 10, 1998 2985 Table 1. Electronic 3dn Configurations at M Cations of AMO3 Perovskites with A ) La, Y, Sr, and Caa perovskite LaTiO3 YTiO3 SrTiO3 CaTiO3 LaVO3 YVO3 SrVO3 CaVO3 LaCrO3 YCrO3 SrCrO3 CaCrO3 LaMnO3 YMnO3 SrMnO3 CaMnO3 LaFeO3 YFeO3 SrFe CaFeO3 LaCoO3 YCoO3 LaNiO3 YNiO3 LaCuO3

configuration π*1σ*0

π*1σ*0 π*0σ*0 π*0σ*0 t2σ*0 t2σ*0 π*1σ*0 π*1σ*0 t3σ*0 t3σ*0 π*2σ*0 π*2σ*0 t3e 1 not perovskite t3σ*0 t3σ*0 t3e 2 t3e 2 t3σ*1 t3σ*1 (1 - x)t6σ*0 + xt4e2 f t5-δσ*1+δ t6σ*0 t6σ*1 t6e 1 t6σ*2

remarks

refb

AF* (138 K), I, O F (30 K), I, O dielectric, I, T-C (110 K) dielectric, I, O AF* (142 K), I, O′-O (137 K) AF* (116 K), I, O′-O (77 K) PP, M, C PP, M, O AF* (290 K), I, O AF* (141 K), I, O PP, M, C AF* (90 K), I, O AF* (100 K), I, O′-O (875 K)

1 1 2 2 3 4 5 5 2

hexagonal polytype AF* (142 K), I, O AF* (750 K), I, O AF* (645 K), I, O F-helix (130 K), M AF (115 K), dis (290 K), O x increases with T smooth I-M, T > 300 K, R diamagnetic, I, O PP, M, R AF (140 K), I, O PP, M, R

2

2 2 2 2 2 2 6 6 7 8 9 1 9

a F ) ferromagnet; AF* ) canted-spin antiferromagnet; PP ) Pauli paramagnet; dis ) disproportionation; I ) insulator; M ) metal; C ) cubic; R ) rhombohedral; O′ ) orthorhombic c/a < x2; O ) orthorhombic c/a > x2; T ) tetragonal; critical temperatures in parentheses. b References: (1) Arima, T.; Tokura, Y. J. Phys. Soc. Japan 1995, 64, 2488; (2) Goodenough, J. B.; Longo, J. M. Landolt-Bo¨ rnstein Tabellen III/4a; Springer-Verlag: Berlin, 1970; p 126. (3) Nguyen, H. C.; Goodenough, J. B. Phys. Rev. B 1995, 52, 324. (4) Ren, Y., et al. Nature, in press. (5) Morikawa, K., et al. Phys. Rev. B 1995, 52, 13711. (6) Gleitzer, C.; Goodenough, J. B. Struct. Bonding 1985, 61, 1. (7) Sen˜arı´s-Rodrı´guez, M. A.; Goodenough, J. B. J. Solid State Chem. 1995, 116, 224. (8) Kappatsch, A.; Quezel-Ambrunaz, S.; Sivardie`re, J. J. Phys. (Paris) 1970, 31, 369. (9) Goodenough, J. B., et al. Mater. Res. Bull. 1973, 8, 647.

Confinement of a hole-rich cluster to a single MO6 complex represents a limiting case of phase segregation that can be difficult to distinguish from a localizedelectron small polaron. More interesting are cases where cooperative J-T or pseudo-J-T oxygen displacements lower the dynamic symmetry of the sites within a multicenter mobile polaron, especially where the concentration of polarons is high enough to lead to condensation of the polarons into a polaron liquid. Characterization of the dynamic structure of such a liquid requires a faster experimental probe than conventional diffraction techniques. However, the formation of multicenter polarons and a polaron liquid at a crossover from localized to itinerant electronic behavior can have a distinctive influence on the physical properties. Space restrictions prevent exposition here of the manifestations of electronic heterogeneity by the large negative magnetoresistance of the manganese and cobalt mixed-valent oxides with perovskite structure and by the normal-state properties of the high-temperature copper-oxide superconductors having perovskite intergrowth structures. V. Representative Single-Valent Perovskites Table 1 summarizes the localized versus itinerant character of the 3dn configurations of the single-valent AMO3 perovskites with first-long-period transition-

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metal atoms M. Configurations tn and em refer to localized electron configurations in a cubic, octahedralsite crystalline field, and the configurations π*n and σ*m refer to itinerant electrons of t-orbital and e-orbital parentage. A. Localized 3dn Configurations. (1) Spin-Spin Interactions. The interatomic spin-spin interactions between localized-electron configurations are described by virtual charge transfers in superexchange perturbation theory.11 In this case, the electron-transfer energy integral (resonance integral) is spin-dependent:

tijvV ) bij sin (θij/2)

and

tijvv ) bij cos (θij/2) (13)

where the bij are given by eq 9 and θij is the angle between spins on neighboring atoms. The superscripts vV and vv refer, respectively, to antiparallel and parallel spins on the two neighboring cations. The spin angular momentum is conserved in an electron transfer. Rules for the sign of the superexchange interactions follow: • Superexchange interactions between half-filled orbitals involve electron transfers to half-filled orbitals, which are constrained by the Pauli Exclusion principle to a tijvV and therefore give a

∆exs ) -|tijvV|2/Ueff ) const + JijSij‚Sij

(14)

where Jij ) (2bij2/4S2Ueff). • Superexchange interactions between half-filled and empty orbitals, where the empty orbitals belong to a localized-electron configuration with a spin S, are not constrained by the Pauli Exclusion Principle, but Hund’s intraatomic exchange field favors, by an energy ∆ex, transfer to a spin state that is parallel to the localized spin of the acceptor cation. In this case tijvv is used in third-order perturbation theory to give

∆exs ) const - JijSij‚Sj

(15)

where Jij ) 2bij2∆ex/(4S2Ueff2). (2) Half-Filled Orbitals. Application of these rules to the localized-electron configurations of Table 1 give antiferromagnetic spin-spin interactions between the t3 configurations and the e2 configurations of LaCrO3, CaMnO3, and LaFeO3. Antiparallel alignment of spins on nearest-neighbor cations gives type-G antiferromagnetic order. In the orthorhombic structure, a Dzialoshinskii vector Dij parallel to the b-axis allows an additional antisymmetric exchange term -Dij‚Si × Sj that cants the spins from θij ) 180° to give a weak ferromagnetic component. (3) Jahn-Teller Ions: Mn3+ versus V3+. Of more interest are the localized t2 configurations at the V3+ ions of LaVO3 and YVO3 or the e1 configurations at the high-spin Mn3+ ions of LaMnO3 because, in each case, the cubic-field symmetry leaves the configuration orbitally degenerate (see Figure 5). As discussed in connection with eq 4, the cubic-field splitting quenches the orbital angular momentum of the 2-fold-degenerate e1 orbitals, but it leaves m ) 0, (1 for the azimuthal orbital angular momentum quantum number of the orbitally 3-fold-degenerate t2 configuration. Therefore, removal of the orbital degeneracy of the Mn3+:t3e1 configuration by a local J-T deformation of the octahedral site to tetragonal or orthorhombic symmetry is

Figure 5. Jahn-Teller removal of orbital degeneracies: (a) e1, tetragonal (c/a > 1) or orthorhombic any T, (b) t2, tetragonal (c/a > 1) or rhombohedral (R > 60°) T > TN, (c) t2, tetragonal (c/a < 1) or rhombohedral (R < 60°) T < TN.

not constrained by spin-orbit coupling, and a cooperative J-T distortion of the lattice may occur in the paramagnetic state. On the other hand, a cooperative J-T distortion that removes the orbital degeneracy of a t2 configuration is constrained by spin-orbit coupling to occur where the spins are ordered nearly collinearly below a magnetic-ordering temperature unless the distortion has a sign that quenches the residual orbital angular momentum (see Figure 5).21 (a) LaMnO3. In LaMnO3, a first-order cooperative J-T distortion of the octahedral sites occurs at a Tt ≈ 875 K; oxygen-atom displacements within the a-b planes create long O‚‚‚Mn‚‚‚O bonds alternating with short O-M-O bonds such that each Mn atom has two short and two long bonds within an a-b plane. The J-T distortion is superimposed onto the cooperative MO6 rotations about a cubic [110] axis responsible for the O-orthorhombic symmetry, so the symmetry remains orthorhombic but with a c/a < x2 as opposed to a c/a > x2 found where only the rotations occur.16,17 The low-temperature orthorhombic phase with c/a < x2 is designated O′-orthorhombic to indicate the presence of a cooperative J-T deformation. The J-T distortion orders the e1 electrons into the long O‚‚‚Mn‚ ‚‚O bonds and empties the e orbital of a short O-Mn-O bond, and the virtual charge transfer across Mn‚‚‚OMn bonds in the a-b planes is from a half-filled to an empty e orbital, which gives a ferromagnetic superexchange interaction according to eq 15. The π-bonding t3 configurations give an antiferromagnetic interaction via eq 14 as in LaCrO3, but weaker π bonding results in a type-A antiferromagnetic order in which ferromagnetic a-b planes are coupled antiparallel to one another along the c-axis.16,17 (b) LaVO3 and YVO3. The orbital angular momentum of the localized V3+:t2 configuration in LaVO3 and YVO3 suppresses any cooperative J-T distortion of the VO6 octahedra in the paramagnetic phase. Spin-orbit coupling also renders the xy and (yz + izx) orbitals each half-filled, so eq 14 applies to give a type-G antiferromagnetic order below the Ne´el temperature TN. Moreover, the Dzialoskinskii vector Dij is larger where the orbital angular momentum is not quenched, so the two perovskites have a canted-spin type-G antiferromagnetic order with a ferromagnetic component in the c-a plane. Ordering of the spins below TN makes possible a cooperative J-T distortion that maximizes the orbital angular momentum; in LaVO3 and YVO3 such a firstorder, cooperative J-T distortion occurs at Tt ) 137 K < TN ) 142 K and Tt ) 77 K < TN ) 116 K,

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Chem. Mater., Vol. 10, No. 10, 1998 2987

transition that enhances the orbital moment at the V3+ ions. A discontinuous change in the orbital moment would induce a response in the persistent atomic currents that give rise to the orbital angular momentum; the response would oppose the change in accordance with Lenz’s law and reverse the direction of the Dzialoshinskii vector on passing through the transition. B. Itinerant 3d Electrons. The situation in SrFeO3 and CaFeO3 is to be contrasted with that in LaMnO3, and the behavior of SrCrO3 and CaCrO3 is to be contrasted with that of LaVO3 and YVO3. Whereas the localized electron configurations have an orbital degeneracy removed by a J-T deformation of the local site symmetry, itinerant electrons occupy one-particle states of the entire crystal; no crystal deformations analogous to the cooperative J-T distortions are found with itinerant electrons. However, the occupied states of an itinerant-electron band may be stabilized relative to unoccupied states by a change of the translational symmetry of the lattice rather than of the point symmetry of a cation site. Changes in the translational symmetry may introduce either a CDW or a spin-density wave (SDW) in the crystal with a propagation vector q. 1. SrFeO3 and CaFeO3. From eqs 9 and 10, the σ* bands of e-orbital parentage have a width

Wσ ≈ 2zσλσ2 cos φ

(16)

where φ is a measure of the bending of the (180° - φ) M-O-M bond angle. Because the t3 configurations of SrFeO3 and CaFeO3 remain localized with a sin S ) 3/2, it is necessary to replace bσcac with the spindependent resonance integral tσvv ) bσcac 〈cos(θij/2)〉, and the bandwidth becomes

Wσ ≈ 2zσλσ2 cos φ〈cos(θij/2)〉

Figure 6. Magnetization curves taken in 1 kOe (a) on heating polycrystalline LaVO3 after cooling to 5 K in 1 kOe from 130 K < Tt, from Tt e 138 K < TN, and from 150 K > TN, and (b) from ref 27, on cooling a single crystal of YVO3 with field along the a-, b-, and c-axes, respectively. Inset of (a): Double peak after cooling from 138 K ≈ Tt shows character of both fieldcooled and zero-field-cooled curves.

respectively.22,23 Remarkably, the phase transition orients the ferromagnetic component in opposition to the internal magnetic field. In LaVO3, the internal field is in the direction of the applied field Ha in the interval Tt < T < TN, and cooling through Tt in Ha induces an anomalously large diamagnetism24,25 (see Figure 6a) that, as was subsequently demonstrated,26 is due to an orientation of the ferromagnetic component in opposition to Ha. Antisymmetric exchange constrains the spins to lie in the c-a plane. In YVO3, a rotation of the crystallographic easy axis of magnetization within the c-a plane reverses the sign of the ferromagnetic component along the a-axis on cooling in the interval Tt < T < TN; and on cooling through Tt, the sign of the magnetization is reversed back into the direction of Ha, as shown in Figure 6b.27 This quite spectacular result appears to be due to the first-order character of the J-T

(17)

where cos φ decreases with the tolerance factor t and therefore with both decreasing temperature and A cation size. In SrFeO3, Wσ remains wide enough that no CDW is formed. However, the intraatomic Hund exchange energy ∆ex polarizes the band-electron spins parallel to the localized spin S ) 3/2 of the t3 configurations in the neighborhood of each cation and introduces an indirect (RKKY) interatomic interaction between localized spins that oscillates from ferromagnetic to antiferromagnetic with increasing separation of the interacting localized spins. Ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions can give rise to a ferromagnetic-helix spin configuration propagating along a cubic [111] axis, and such a configuration with a |q| ) 0.112(2π/ao) has been observed by neutron diffraction.28 Substitution of a smaller Ca for Sr increases φ, which narrows Wσ, and below 290 K the disproportionation reaction

2Fe4+ ) FeI(4-δ)+ + FeII(4+δ)+

(18)

sets in smoothly with δ increasing toward unity with decreasing temperature.15 This disproportionation reflects the concentration of the itinerant-electron character in molecular orbitals of FeIIO6 and the introduction of a localized-electron character at the FeI atoms. This

2988 Chem. Mater., Vol. 10, No. 10, 1998

behavior is but one possible response to the approach to localized-electron behavior as an itinerant-electron bandwidth is narrowed. 2. SrCrO3 and CaCrO3. Substitution of Ca for Sr narrows a π* bandwidth, as illustrated by the chromates in Table 1. Whereas SrCrO3 remains a Pauli-paramagnetic metal to lowest temperatures, CaCrO3 becomes antiferromagnetic with a TN ≈ 90 K. The itinerant character of the antiferromagnetism of CaCrO3 has been demonstrated by a dTN/dP < 0;29 a dTN/dP > 0 for localized t2 configurations follows from eq 14 because bij increases and Uπeff ) Uπ decreases with hydrostatic pressure P. The sign of the interatomic spin-spin interactions does not change with the breakdown of the superexchange perturbation theory associated with localized electrons, but the sign of dTN/dW does change.30 On the other hand, these experiments tell us little about whether the character of the electrons changes smoothly or abruptly on passing from itinerant to localized character. 3. Sr1-xCaxVO3. According to the virial theorem, we may anticipate an abrupt transition from strongly correlated, itinerant quasiparticles to localized electrons. In a single-valent system, such an abrupt transition could manifest itself as a global dilatation of the lattice on passing from itinerant to localized electronic character. Such a transition is observed in the quenchedin B81 phase of NiS.31 Alternatively, it could manifest itself in the perovskite structure as localized-electron fluctuations in an itinerant-electron matrix, with cooperative oxygen displacements stabilizing localizedelectron domains of larger mean M-O bond length that fluctuate over time. Observation of such dynamic fluctuations would require a fast experimental probe. One such probe is photoemission spectroscopy (PES). Morikawa et al.32 have performed an elegant study of SrVO3 and CaVO3 with inverse photoemission and high-resolution PES. SrVO3 and CaVO3 are both Pauliparamagnetic metals, but Wπ is narrowed by the substitution of Ca for Sr just as in the chromates. CaVO3 becomes antiferromagnetic with only small deviations from stoichiometry, which indicates that the transition from itinerant to localized electronic behavior is being approached from the itinerant-electron side. The PES data show the coexistence of two d-electron spectra: one corresponds to incoherent (localized-electron) states at energies well below the Fermi energy F and the other to coherent (itinerant-electron) states with a sharply defined Fermi surface (see Figure 7). Moreover, Figure 7 shows a significant transfer of states from the coherent to the incoherent spectrum in CaVO3 compared with SrVO3 as should be expected for narrower π* bands in CaVO3. These data demonstrate that, in the absence of a static phase segregation into localized-electron configurations and molecular-orbital clusters, as appears to occur in CaFeO3, there can be a dynamic segregation into localized-electron configurations within a matrix containing itinerant electrons without the stabilization of a global, itinerant-electron antiferromagnetic or SDW phase. This behavior is quite different from the Mott-Hubbard picture33 of a smooth, global opening of an energy gap as the bandwidth of a single-valent system narrows from that of a Pauliparamagnetic metal to that of a magnetic insulator.

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Figure 7. High-resolution photoemission spectra taken at T ≈ 30 K.32 Dashed curves are decomposition of the tail of the O-2p valence band and the incoherent part of the V-3d spectrum. Solid curves are densities of states of coherent spectral weight taken from an LDA band-structure calculation narrowed by a factor mb/m*.

Figure 8. Schematic variation of a normalized effective mass versus the normalized Hubbard energy U for a mass-enhanced metal. Deviation from Brinkman-Rice (dashed) curve occurs where coherent and incoherent states coexist.

Similar measurements and analysis of the Sr1-xCaxVO3 system34 show a continuous transfer of states with increasing x from the coherent to the incoherent spectrum. It is also possible to extract from the PES data a measure of the ratio m*/mb, where m* and mb are, respectively, the effective and bare mass of the itinerant electrons; the data show a ratio of m*/mb that passes through a maximum value with increasing x. Brinkman and Rice35 have predicted a ratio

m*e-e/mb ) [1 - (Ueff/Uc)2]-1

(19)

for a strongly correlated, globally homogeneous system of electronic quasiparticles. This ratio is plotted in Figure 8. Also shown is the implication of the PES data; viz., a departure from the Brinkman-Rice prediction

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Chem. Mater., Vol. 10, No. 10, 1998 2989

Figure 9. Temperature dependence of the Seebeck coefficient R(T) of (a) CaVO3 and (b) Pt under different hydrostatic pressures P in a self-clamped device. Lower insets: R(room T) versus P. Upper inset of (a): fitted curves corrected for a uniform P over temperature.

where the homogeneous system breaks down into a heterogeneous electronic system and me-e*/mb reaches a maximum within the range Uc-Uπeff, where localized and itinerant electrons coexist. To test whether the maximum in m*/mb found in the Sr1-xCaxVO3 system is a true reflection of the approach of Uπeff ) Uπ to Uc, as indicated in Figure 8, or is a consequence of the presence of two different isovalent A cations, we36 studied the temperature dependence of the thermoelectric power, R(T), of CaVO3 as a function of hydrostatic pressure P. The thermoelectric power of a polycrystalline sample is a transport property that is not affected by the grain boundaries. Hydrostatic pressure increases the bandwidth Wπ and reduces Uπ/Uc, which is why m*/ mb would decrease with applied pressure in a conventional homogeneous electronic system. CaVO3 is chemically homogeneous, and the PES data would place Uπ close to Uc in Figure 5. If the maximum in m*/mb indicated in Figure 8 is representative of a heterogeneous electronic system, reduction of Uπ/Uc by pressure in CaVO3 should increase m*/mb, contrary to the prediction for a homogeneous system. Figure 9 shows the results of our pressure experiments on CaVO3. Interpretation of Figure 9 begins with a general expression for the thermoelectric power:

R ) R0 + δR

(19)

where δR is a low-temperature enhancement or phonondrag component. Above room temperature, R ≈ R0 where

Ro ) -

k e

∫

( - F) σ() d kT σ

(21)

in which σ() ) f()[1 - f()]N() µ() is the product of the Fermi distribution function f(), the energy density of one-particle states N(), and the particle mobility

µ() at an energy  relative to a band edge. In a metallic conductor, Ro becomes Mott’s expression

Ro ≈ -

{

}

π2k2T ∂ ln σ() 3eF ∂ ln 

)F

(22)

A band-structure calculation37 indicates the Fermi surface is not strongly perturbed by its interaction with the Brillouin-zone boundary, so the factor {∂ ln σ()/∂ ln })F should be insensitive to volume changes. In this case, the pressure sensitivity of Ro for an electron gas varies as 1/F ∼ V2/3. Electron-phonon interactions of coupling strength λ introduce into R a factor (1 + λ) that is also pressure dependent.38 In a homogeneous electronic system, this factor gives rise to an effective mass m*e-ph that is calculated by a similar renormalization procedure as that used by Brinkman and Rice35 to obtain m*e-e/mb due to electron-electron interactions. Therefore we assumed that m*e-e/mb adds another pressure-dependent factor to R, and we considered the pressure dependence of

R ≈ (m*e-e/mb)(1 + λ)Ro

(23)

Broadening of a bandwidth by the application of hydrostatic pressure reduces the curvature of (k) so as to reduce (1 + λ) as well as the volume V. Moreover, placement of Uπ/Uc to the left of the maximum in m*e-e/ mb in Figure 8 would also give rise to an m*e-e/mb that decreases with pressure, so we could predict unambiguously a ∂|R(300 K)|/∂P < 0 for a conventional metal with a homogeneous electronic system, which is what was observed in Figure 9 for R(300 K) of Pt. On the other hand, Figure 9 shows a ∂|R(300 K)|/∂P > 0 for CaVO3, which can only be explained within the framework of the previous discussion if m*e-e/mb increases with the bandwidth (i.e., with decreasing Uπ/Uc). This finding is consistent with the analysis of the PES data, which

2990 Chem. Mater., Vol. 10, No. 10, 1998

found a maximum in m*/mb with increasing x in the system Sr1-xCaxVO3. We conclude that the maximum in m*/mb is an intrinsic property of a heterogeneous electronic system and is not an artifact of the presence of two A cations of different size. The other significant feature of Figure 9 is the difference in the effect of hydrostatic pressure on the phonon-drag term δR for Pt and CaVO3. At ambient pressure, both Pt and CaVO3 show a phonon-drag enhancement with a Tmax ≈ 60 K that is characteristic of a metal with a Tmax ≈ 0.2θD, where θD is the Debye temperature. This enhancement becomes negligible at room temperature because δR/R0 ∼ T-2.39 A modest electron-phonon coupling parameter λ and long-range acoustic phonons are prerequisites for the phonon-drag effect. In the pressure range of our experiments, pressure would produce a negligible change in λ and θD, so no appreciable change in either Tmax or the magnitude of δR can be anticipated for a homogeneous electronic system, as is demonstrated for Pt. On the other hand, the magnitude of δR in CaVO3 is seen to increase dramatically with pressure, a response that can only, to our knowledge, be understood if pressure increases the correlation length of the phonons. This deduction is also consistent with the PES evidence for a heterogeneous electronic system in which the concentration of localized-electron fluctuations decreases with increasing bandwidth. Localized-electron fluctuations would enhance a Pauli-paramagnetic susceptibility; they need not introduce a Curie-Weiss type of temperature dependence. We therefore conclude that suppression of δR in a chemically homogeneous metallic system is a signature of an electronically heterogeneous system and that the diagram of Figure 8 is qualitatively correct. 4. The La1-xNdxCuO3 System. Metallic LaCuO3, which is prepared under high oxygen pressure,40 has a narrow, half-filled σ* band; it exhibits an enhanced Pauli-paramagnetic susceptibility that has been interpreted41 to be due to a Brinkman-Rice enhancement of m*e-e associated with a Ueff ) Uσ approaching Uc. Substitution of the smaller Nd3+ ion for La3+ decreases the (180° - φ) Cu-O-Cu bond angle, which from eq 16 narrows Wσ without changing the oxidation state of the CuO3 array. In an attempt to narrow Wσ to the limit Uσ ) Uc, La1-xNdxCuO3 samples were prepared under high oxygen pressure; but single-phase samples could only be obtained over the range 0 e x e 0.5.42 We were not able to obtain a high-pressure phase that converted at ambient pressure to a localized-electron phase. Nevertheless, the enhancement of the Pauli-paramagnetic susceptibility increased with x, as anticipated, and the samples remained metallic for all x. Figure 10 shows plots of R(T) under different hydrostatic pressures P for samples x ) 0, 0.25, and 0.5 of the system La1-xNdxCuO3 for comparison with the data of Figure 9 for CaVO3. Of particular interest is the value of R(300 K) and the change with x and P in the magnitude of the phonon-drag component δR, which is negative in this system. The magnitude of R(300 K) for all x is as small as that of elemental copper, which distinguishes these copper oxides from other metallic oxides with partially filled σ* bands. From the Mott expression (eq 22), a small Ro(300 K) indicates either little curvature of the (k) dispersion curves at F or a

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Figure 10. Temperature dependence of the thermoelectric power R(T) of La1-xNdxCuO3 under different pressures for (a) x ) 0, (b) x ) 0.25, and (c) x ) 0.5

fortuitous cancellation of positive and negative contributions coming from different parts of the Fermi surface. A significant, positive R(300 K) would be predicted from the calculated43 band structure for LaCuO3, which casts doubt on the homogeneous quasiparticle assumption on which the band-structure calculation was based. Moreover, the Nd-doped samples exhibit a small increase in Ro(300 K) with pressure and a decrease with increasing Nd concentration x; both of these observations indicate m*e-e/mb increases with

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increasing bandwidth Wσ as in the case of CaVO3, which would locate the x ) 0.5 sample near the Uσeff ) Uc boundary in Figure 8 and the x ) 0 sample near the bandwidth with a maximum m*e-e. Moreover, the phonon-drag component δR(T) is gradually suppressed as x increases at atmospheric pressure; it nearly disappears in the x ) 0.5 sample. However, the magnitude of δR(T) increases with P. Because high pressure would have no influence on an impurity-scattering mechanism, we are forced to conclude, as for CaVO3, that strong heterogeneous electron-lattice interactions progressively reduce the phonon coherence length with decreasing width of the conduction band. Thus, Figure 8 appears to apply to the narrow-band system La1-xNdxCuO3 as well as to Sr1-xCaxVO3. C. Crossover without Coexistence of Localized Spins. The LnTiO3 and LnNiO3 families in which Ln is a trivalent lanthanide or yttrium provide examples of single-valent perovskites at the crossover from itinerant to localized electronic behavior. The TiO3 array contains Ti3+:π*1σ*0 configurations with quasi-degenerate π* bands of t-orbital parentage that are one-sixth filled, a configuration that is analogous to the VO3 array of the Sr1-xCaxVO3 system. The NiO3 array contains low-spin Ni(III):t6σ*1 configurations with 2-fold-degenerate σ* bands of e-orbital parentage that, as in the case of SrFeO3 and CaFeO3, are one-quarter filled. However, in the NiO3 array, the σ*-band electrons do not coexist with a localized spin on a t3 configuration, but with a filled t6 configuration. (1) LnTiO3 (Ln ) Rare-Earth or Yttrium). LaTiO3 is semiconductive with a strongly enhanced Pauli paramagnetism at temperatures T > TN ≈ 138 K; below a second-order transition at TN, it becomes a weakly ferromagnetic semiconductor with a canted-sin type-G antiferromagnetic order and a semiconductive energy gap Eg ≈ 0.2 eV.44 PES data of Fujimori et al.45 show a small fraction of coherent states coexisting with a large fraction of incoherent states. YTiO3, on the other hand, is a ferromagnetic insulator with an energy gap Eg ≈ 1.2 eV and a Curie-Weiss paramagnetism above Tc ≈ 30 K.46 The PES data for this perovskite show only incoherent electronic states are present; but there is no J-T deformation below Tc of the O-orthorhombic structure as occurs in LaVO3 and YVO3 structure where the t2 configuration is localized. In a single-valent, electronically homogeneous MO3 array, strong electron-electron interactions within narrow, degenerate bands that are less than one-quarter filled have been predicted47 to give itinerant-electron ferromagnetic order in a semiconductive phase with a band gap Eg ) U - W without any localized-electron J-T deformation below Tc. The ferromagnetic order of YTiO3 with an Eg ≈ Uπ - Wπ ) 1.2 eV fits this description. In a homogeneous ferromagnetic system, the paramagnetic susceptibility obeys a Curie-Weiss law. The larger (180° - φ) Ti-O-Ti bond angle in LaTiO3 and the more ionic character of the La-O bond relative to the Y-O bond broaden the π* bands of LaTiO3 relative to those of YTiO3. Consequently, the electronelectron interactions are weaker in LaTiO3; nevertheless, they remain strong enough to retain a Uπ g Uc. In CaVO3, a Uπ < Uc relationship leaves the electronic

Chem. Mater., Vol. 10, No. 10, 1998 2991

Figure 11. Magnetic phase diagram for La1-xYxTiO3.51

system Pauli paramagnetic, but enhanced, to lowest temperatures; in LaTiO3, an enhanced Pauli paramagnetism is retained above TN, but a Uπ g Uc relationship induces magnetic order below TN. The PES data45 for LaTiO3 demonstrate that the heterogeneous character of the electronic system found in CaVO3 persists in LaTiO3 across the critical bandwidth where Uπ ) Uc. Above TN, the fluctuating moments associated with incoherent states strongly enhance the Pauli-paramagnetic susceptibility of the electronic system without introducing a Curie-Weiss temperature dependence as in CaVO3.48 However, below TN stabilization of a SDW locks these moments into a static spin configuration. Stabilization of the SDW opens a gap Eg ) Uπ - Wπ at the Fermi energy in the coherent-state band to give a small Eg ≈ 0.2 eV. The evolution of the magnetization with decreasing bandwidth Wπ can be obtained by varying the angle φ of the (180° - φ) Ti-O-Ti bond angle. The angle φ decreases with the size of the rare-earth ion Ln in the family LnTiO3 and with x in the system La1-xYxTiO3. Chemical homogeneity is preserved in the LnTiO3 family, but the magnetic moments of the rare-earth ions change. The evolution of the magnetic properties of the TiO3 array with changing φ is similar for the LnTiO3 family and the La1-xYxTiO3 system, which indicates any interaction between the rare-earth magnetic moments and the π* electrons is weak. The Ne´el temperature TN decreases with increasing φ from 138 K for LaTiO3 to ∼50 K in SmTiO3;49 europium is present as Eu2+ in EuTiO3, and by GdTiO3 the TiO3 array has become ferromagnetic with a Tc ≈ 34 K.50 Figure 11 shows the evolution with x of TN and TC in the La1-xYxTiO3 system.51 Raman scattering52 indicates that TN decreases with the coherent-electron density at the Fermi energy F, which is consistent with a stabilization of the antiferromagnetic phase by the formation of a SDW. Optical spectra53 show a sharpening of the incoherentband absorption edge with a decrease in the fraction of coherent states as (180° - φ) decreases. It follows from these data that the pressure dependence dTN/dP > 0

2992 Chem. Mater., Vol. 10, No. 10, 1998

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perturbation expansion of eq 5 for the crystal-field wave function ψe. The result is a massive covalent mixing of Ni-e and O-2pσ orbitals in the itinerant-electron σ*-band states corresponding to an equilibrium reaction

Ni(III):σ*1 + O2-:pσ2 ) Ni2+:e2 + O-:pσ1

Figure 12. Magnetic and electronic T - t phase diagram for the LnNiO3 family, according to ref 55.

observed54 for LaTiO3 does not reflect the pressure dependence of the superexchange interaction of eq 14 for localized spins on the Ti3+ ions, but a transfer of spectral weight from incoherent to coherent states with increasing Wπ, which increases the density of coherent states at F. (2) LnNiO3 (Ln ) Rare-Earth or Yttrium). The LnNiO3 family undergoes a transition from an enhanced Pauli paramagnetism in metallic LaNiO3 to a CurieWeiss paramagnetism with antiferromagnetic order below a TN in the insulators LuNiO3 and YNiO3. Figure 12 shows the evolution with tolerance factor t of a global first-order insulator-metal transition TIM and the Ne´el temperature TN.55 With the exception of LaNiO3, all the perovskites have the O-orthorhombic structure at room temperature; an orthorhombic-rhombohedral transition occurs at a TOR > TIM. On cooling through TIM, the volume expands by 0.2% as a result of a small increase in the average Ni-O bond length of ∼0.004 Å; the Ni-O-Ni bond angles decrease by ∆θ ≈ -0.5°.56 However, no reduction in the symmetry of the local NiO6 octahedra could be detected by neutron diffraction, and the crystal symmetry remained O-orthorhombic across TIM. The magnetic transition at TN < TIM is secondorder, but it is first-order in NdNiO3 and PrNiO3, where TN ) TIM. Below TN, the antiferromagnetic order is unusual;57,58 it can be represented as a SDW propagating along a [111] axis with Ni-O-Ni spin-spin interactions that alternate between ferromagnetic and antiferromagnetic; the nickel moment obtained by neutron diffraction is µNi ≈ 0.9µB, but it appeared to increase to 1.2µB in EuNiO3. An isotope exchange of 18O for 16O had no effect on the structure or on TN < TIM and the orthorhombic-rhombohedral transition temperature TOR > TIM, but it increased TIM significantly:59 ∆TIM ) TIM(18O) - TIM(16O) ) +10.3, +8.5, +7.6, +3.1, and +1.7 K for Ln ) La0.1Pr0.9, Pr, Nd, Sm, and Eu, respectively. Moreover, TIM(16O) decreases and ∆TIM increases linearly with cos φ ∼ Wσ. Interpretation of these quite remarkable findings begins with the observation that the Ni(III) ions are in their low-spin configuration t6σ*1 and that a Ni(III)/Ni2+ redox energy lies close to the O2-:2p6 energy level in an ionic model; an ionic model has a charge-transfer gap ∆ ≈ 0, which means there is a breakdown of the

(24)

that is not biased strongly to either the left or the right. A natural interpretation60 of the unusual antiferromagnetic order below TN in the insulator phase follows from eq 24: The insulator phase represents a CDW electronic segregation into more strongly covalent Ni-ONi interactions alternating with more ionic Ni-O-Ni interactions. Below TN, the more covalently bonded NiO-Ni layers couple ferromagnetically via a covalentexchange interaction in which the parallel-spin electron O-pσ(v) occupies a molecular orbital of a Ni-O-Ni bond to couple parallel the Ni-e(v) of the two neighboring Ni atoms via an intrabond direct-exchange interaction between electrons in orthogonal molecular orbitals. The 2-fold e-orbital degeneracy at the Ni(III) atoms makes possible the preferential transfer of O-pσ(v) electrons into the empty e(v) orbitals. On the other hand, the ferromagnetic Ni-O-Ni layers are coupled antiferromagnetically by superexchange coupling across the more ionic O2- ions that separate them. The CDW in the insulator LnNiO3 phases is to be contrasted with the negative-U CDW that develops in CaFeO3. In CaFeO3, covalent bonding is concentrated in an FeIIO6 complex and parallel-spin electrons are transferred to a more ionically bonded FeI(4-δ)+ ion (eq 18). Which of these CDWs is the more stable depends on the relative energies of Uσ and ∆ for the two systems; it appears that a Uσ < ∆ controls the CDW formation in CaFeO3, and a ∆ < Uσ in the LnNiO3 family. It is also to be noted that LaNiO3 is a bad metal and that the first-order transition at TIM in PrNiO3 exhibits a large isotope shift. These observations suggest that the static CDW postulated for the insulator phase becomes dynamic in the “bad-metal” phase with a retention of strong electron interactions with optical phonons. A transition from a static to a dynamic CDW would, according to the virial theorem, be compatible with the first-order transition at TIM and a larger mean Ni-O bond length in the insulator phase. It is also consistent with the large isotope shift of TIM, a heavier oxygen mass stabilizing the static CDW to a higher TIM. Moreover, a narrower Wσ would increase TIM, but reduce the kinetic energy of the mobile CDWs in the “metallic” phase so as to reduce ∆TIM and the volume change ∆V at TIM. Pressure has a dramatic effect on TIM; a common rate of decrease dTIM/dP ) -4.2 K/kbar has been reported,61 a broader Wσ decreasing TIM. In this family, a dt/dP > 0 shows that the equilibrium Ni-O bond length is unusually compressible, signaling a doublewell potential for the equilibrium bond length at the crossover from localized to itinerant electronic behavior. Above TIM, strong coupling of electrons to optical phonons gives rise to “vibronic” states. Vibronic states in a phase with a dynamic CDW appears to be a characteristic feature of partially filled σ* bands as we have argued elsewhere occurs in the mixed-valent manganese-oxide perovskites exhibiting a “colossal” negative magnetoresistance.62-64

Reviews

Chem. Mater., Vol. 10, No. 10, 1998 2993

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